Surface coating of sutures and allied medical products has been the subject of extensive interest in the prior art as it relates mostly to improved surface aesthetics and handling characteristics and reduction of capillarity in braided multifilaments as reviewed in U.S. Pat. No. 4,461,298 (1984), which was uniquely directed to minimizing the tissue-reaction encountered in commercially available silk sutures due to components of commonly used silk suture coatings. Several reports of the prior art also addressed the use of coating on multifilament braided sutures as a vehicle for the controlled release of antimicrobial agents, among others which have been randomly described, in part, in a number of patents including U.S. Pat. Nos. 3,987,797; 4,027,676; 4,105,034; 4,185,637; 4,201,216; and 4,461,298. In effect, the selections of the coatings, with or without bioactive agents, as described in the prior art were based primarily on a trial-and-error approach without integrating conceptual designs of useful (1) surface coatings tailored for specific suture geometry (being a monofilament or multifilament) and unique surface chemistry (being polar or non-polar and permanent or transient); (2) coatings that are capable of predictable and controllable release of a specific agent based on molecular dispersity of such an agent in the polymer; (3) coatings that can be easily and reproducibly applied to the suture without compromising its initial physicomechanical properties; (4) coatings that do not chemically react with an added bioactive agent and alter its intended bioactivity; and (5) coatings that can be used as a vehicle for incorporating at least one bioactive agent in a molecularly dispersed form while remaining independently efficacious. Reviewing the noted deficiencies of the prior art and availability of patented polymeric compositions developed in this laboratory, including those on polyesters displaying autocatalyzed hydrolysis and segmented polyaxial and linear copolyesters (U.S. Pat. Nos. 5,522,842; 5,773,563; 6,462,169; 6,498,229; 6,703,035; 6,794,485; 7,026,437; and 7,070,858), and acknowledging the growing interest in meeting the surgical needs of a broad spectrum of patients of acknowledged diversity in age and ailment provided a strong incentive to pursue the subject of the present invention. Indeed, the subject invention uniquely integrates key chemical, physicomechanical, biological, and pharmacological aspects pertinent to the use of drug-containing coatings to produce highly efficacious suture products having suture-specific coatings for modulated release of at least one bioactive agent.